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Answer:
x=a^2. y=b^2
Step-by-step explanation:
Answer:
x=a^2. y=b^2
Step-by-step explanation:
\begin{lgathered}\frac{x}{a} + \frac{y}{b} = a + b \\ \frac{xb + ya}{ab} = (a + b) \\ bx + ay = (a + b)ab \: ...........1 \\ \\ \frac{x}{ {a}^{2} } + \frac{y}{ {b}^{2} } = 2 \\ \frac{x {b}^{2} + y {a}^{2} }{ {a}^{2} {b}^{2} } = 2 \\ x {b}^{2} + y {a}^{2} = 2 {a}^{2} {b}^{2} \: .............2 \\ now \: solving \: the \: eqs\: we \: have \\ eqs \: 1 \times a = abx + {a}^{2} y = (a + b) {a}^{2} b \: \\ subtracting \: eqs \: 2 \: x {b}^{2} + y {a}^{2} = 2 {a}^{2} {b}^{2} \\ so \: we \: get \: abx - x {b}^{2} = (a + b) {a}^{2} b - 2 {a}^{2} {b}^{2} \\ xb(a - b) = {a}^{2} b(a + b - 2b) \\ x = \frac{ {a}^{2} b(a - b)}{(a - b)b} = {a}^{2} \\ \\ now \: putting \: the \: value \: of \: x \: \: in \: eqs \: 2 we \: get \\ {a}^{2} {b}^{2} + y {a}^{2} = 2 {a}^{2} {b}^{2} \\ y {a}^{2} = {a}^{2} {b}^{2} \\ y = \frac{ {a}^{2} {b}^{2} }{ {a}^{2} } = {b}^{2}\end{lgathered}
a
x
+
b
y
=a+b
ab
xb+ya
=(a+b)
bx+ay=(a+b)ab...........1
a
2
x
+
b
2
y
=2
a
2
b
2
xb
2
+ya
2
=2
xb
2
+ya
2
=2a
2
b
2
.............2
nowsolvingtheeqswehave
eqs1×a=abx+a
2
y=(a+b)a
2
b
subtractingeqs2xb
2
+ya
2
=2a
2
b
2
sowegetabx−xb
2
=(a+b)a
2
b−2a
2
b
2
xb(a−b)=a
2
b(a+b−2b)
x=
(a−b)b
a
2
b(a−b)
=a
2
nowputtingthevalueofxineqs2weget
a
2
b
2
+ya
2
=2a
2
b
2
ya
2
=a
2
b
2
y=
a
2
a
2
b
2
=b
2